Search

ABSTRACT In this paper, we study the exponential tracking and disturbance rejection problem of a class of Euler–Lagrange (EL) systems with high‐order actuator dynamics. This type of EL system takes into account not only the dynamics of the rigid components of the plant but also the dynamics of the actuators and it includes the elastic joint robot manipulator as a special case. Assuming the reference signal is bounded with bounded derivatives and both the output and the input of the actuator are subject to multi‐tone sinusoidal disturbances, we first establish nonlinear observers for the unknown disturbances based on the internal model principle. Then, we further construct a control law through a backstepping‐like design procedure to achieve the exponential tracking and disturbance rejection for the class of EL systems with high‐order actuator dynamics. A numerical example is provided to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

A wide range of practical control systems such as robot manipulators and spacecrafts can be modeled by Euler–Lagrange systems. On one hand, the requirements for system control accuracy, response speed, and robustness are ever increasing. On the other hand, the control performances are inevitably degraded by multiple disturbances. In this paper, a novel finite‐time composite control law is proposed for a class of Euler–Lagrange systems subject to multiple heterogeneous disturbances including a neutrally stable disturbance and a norm‐bounded disturbance. More specifically, a refined sliding mode disturbance observer (RSMDO) is proposed to estimate and reject the neutrally stable disturbance in the feedforward channel, while an adaptive nonsingular backstepping control (ANBC) is designed in the feedback channel to stabilize the system and attenuate the observer error as well as the norm‐bounded disturbance. The proposed RSMDO can not only fully utilize the disturbance information, but also quantify the convergence time and steady‐state accuracy of the estimation error. The finite‐time stability analysis is carried out for the closed‐loop system. Finally, an example of spacecraft attitude control system is given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed optimization problem of networked Euler–Lagrange (EL) systems with actuator faults and unknown model parameters. In order to solve this issue, some event‐triggered fault‐tolerant (ETFT) optimal coordination algorithms with the mechanism of intermittent communication and intermittent controller update are designed for the first time to compensate for the impact of physical faults on the system, and reduce communication costs and control resource consumption. For practical applications, it is difficult for the system to have a secure environment if there exist malicious attacks blocking network channels among agents. Therefore, the resilient ETFT optimal coordination with intermittent communication subject to asynchronous denial‐of‐service (DoS) attacks is considered. Especially, auxiliary systems with adaptive gains are introduced in the algorithms due to the unavailability of the EL model parameters, which also enable virtual data exchange between agents and protect actual state information. Note that the algorithms are fully distributed as the global topology information is not required. Finally, the feasibility of the proposed algorithms is verified through numerical simulation of examples. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of sampled‐data practical tracking for Euler‐Lagrange systems subject to uncertain parameters. We assume that the system matrix of the exosystem and the Euler‐Lagrange system both contain unknown parameters, which is clearly more practical. The existence of unknown system parameters invalidates existing control strategies and poses a major challenge to the solvability of the problem. With the help of the internal model principle and the adaptive control technology, we propose a novel sampled‐data dynamic compensator to overcome the challenge of unknown parameters in exosystems. In particular, a virtual sampling adaptive control input is proposed to deal with uncertainties in the exosystem matrix. Then, a sampled‐data control law is constructed to guarantee that, by any fast predefined rate, the tracking error exponentially approaches any small predefined ranges of the origin, thus ensure the tracking performance. Finally, we apply our result to a three‐link robot manipulator system. [ABSTRACT FROM AUTHOR]

This article investigates the robust tracking control problem for a class of Euler–Lagrange systems in presence of parameter uncertainties and external disturbances. Through system transformation and theoretical analysis, an adaptive dynamic programming (ADP) algorithm with two adaptive neural networks (NNs) and a suitable triggering mechanism is proposed to attain the robust stability of the closed‐loop system. A single critic NN is leveraged to implement the approximate optimal controller design. Particularly, an NN‐based feedforward compensation is developed to cope with the uncertainties with unknown bounds. Two different triggering mechanisms are respectively constructed to reduce the budget of sampling, communication and computation, namely the dynamic event‐triggering mechanism (DETM) and the self‐triggering mechanism (STM). The DETM is utilized to decide the update of remote controller and critic NN weight, which can yield a larger inter‐event interval than the static event‐triggering mechanism. Also, the Zeno‐free behavior is guaranteed. Moreover, it is a novel attempt to introduce the STM into ADP design, which relaxes the demand of dedicated hardware online monitoring the event‐triggering condition. Then it is demonstrated that all signals in the closed‐loop system are uniformly ultimately bounded (UUB) via Lyapunov‐based stability analysis. Finally, a simulation example of 2‐link robotic system is implemented to verify the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Every closed-loop system holds a level of fault tolerance, which could be increased by using a fault tolerant control (FTC) scheme. In this paper, an efficient FTC scheme for a class of nonlinear systems (Euler–Lagrange ones) is proposed, which guarantees high performance and stability in a faulty system. This scheme was designed on the basis of a cascade control structure in which the inner loop is the closed-loop system and the external loop is the FTC, a generalized proportional integral (GPI) observer-based controller, which manages the fault tolerance level increment. An important issue of the proposed scheme is that the GPI observer-based controller jointly estimates disturbances and faults, providing information about the state of health of the system, and then compensates their effect. The scheme is efficient because only the inertia matrix is required for the controller design, it is able to preserve the nominal control law unchanged and can operate properly without explicit information about system faults (fault diagnostic module). Simulation results, on a pendulum model, show the effectiveness of the proposed scheme for tracking control.

This article studies the problem of structure-free distributed containment control for uncertain underactuated multiple Euler-Lagrange systems (MELSs) considering disturbances by using a layered approach. First, the second layer is the virtual layer constructed artificially for hierarchical control. We move all virtual nodes to the convex hull formed by leaders in the first layer by implementing containment control algorithms on all virtual nodes. Then, the third layer is the following layer, and we propose an adaptive robust tracking controller to ensure that each follower in the third layer tracks the corresponding virtual node in the second layer. So far, the underactuated MELSs can achieve containment control. Furthermore, through the theoretical derivation, sufficient conditions are obtained to achieve the objective of structure-free containment control. Finally, the effectiveness of the proposed stratified structure-free containment control method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function. [ABSTRACT FROM AUTHOR]

In this manuscript, the regulation of one degree-of-freedom Euler–Lagrange systems subject to input saturation is addressed. In particular, the design and analysis of a nonlinear static state feedback controller is presented. As a result, it is proven via Lyapunov's direct method that, in the presence of Rayleigh dissipation, the closed-loop equilibrium point is globally asymptotically stable with a strict Lyapunov function. Since saturation occurs in the system which contains the actuator model, the proposed control law is unconstrained and can be simplified to a proportional-derivative with desired gravity compensation algorithm. As a by-product global asymptotic stability is also proven for the case where Rayleigh dissipation is null. Numerical simulations on a crank-slider mechanism are presented. Moreover, experimental results on a DC-DC buck power converter are also shown and confirm the viability of our approach. [ABSTRACT FROM AUTHOR]

In this work, a new control structure for fully actuated systems that solve the regulation and tracking of trajectories problem is proposed. This controller stands out for its ease of implementation and its ability to attenuate disturbances caused by parametric uncertainties and external forces. The control structure is based on the estimation of the delayed disturbances. Then, the current disturbance is canceled with the delayed disturbance, via the control input. The way in which the dynamics of the system is affected by the residual of these disturbances is analyzed. Also, the necessary conditions for establishing a reduced overshoot, settling time, and an attenuation factor of the disturbance are obtained. The performance of the proposed control structure is illustrated numerically by analyzing the behavior of different second-order single-input–single-output systems and also in the case of a RR-type robot. The control structure was also experimentally implemented in the case of a birotor type drone. [ABSTRACT FROM AUTHOR]

The problem of event‐triggered finite‐time trajectory tracking control of perturbed Euler–Lagrange systems with nonlinear dynamics and disturbances is addressed in this article. Extreme learning machine (ELM) framework is employed to formulate unknown nonlinearities, and adaptive technique is adopted to adjust output weights of the ELM networks and remedy the negative impacts of disturbances, nonlinearities, and residual errors. Then to ensure the system follows the desired position trajectory within a finite‐time, an adaptive ELM‐based sliding mode control strategy is developed. Moreover, event‐triggered control technique is proposed to regulate control outputs on the basis of the developed control strategy for reducing actuator actions and saving communication resources. Lyapunov stability theorem is utilized to confirm bounded trajectory tracking results and finite‐time convergence of the Euler–Lagrange system. Finally, the effectiveness of the developed adaptive ELM‐based event‐triggered sliding‐mode control strategies is substantiated by simulations in a robotic manipulator system. [ABSTRACT FROM AUTHOR]

A generalised proportional-derivative type scheme for the finite-time and exponential tracking continuous control of Euler–Lagrange systems with input constraints is developed. Its generalised design permits the choice among multiple saturating structures. Suitable functions are involved for the appropriate shaping of every error correction term, and complementarily of their addition, to achieve the concerned type of convergence (in addition to the input saturation avoidance). Such a shaping is carried out through control parameters that act as exponential weights on the gained configuration and generalised velocity errors and on their joint action. Compared to previous finite-time approaches, such exponential weights are required to satisfy generalised comparative conditions, avoiding a fixed equivalence relation among any of them. This permits to give rise to a wider spectrum of finite-time convergent closed-loop trajectories and gives an optional type of (unconventional) exponential convergence (in addition to the conventional one). The resulting extended conditions on the exponential weights and the generalised saturating structure enlarge the controller potential for performance improvement or adjustment. The generalised design is supported through a more general analysis based on more general strict Lyapunov functions, stating more solid analytical bases for possible design extensions on the accomplishment of other control objectives. The study is further supported through experimental tests on a 3-degree-of-freedom robot manipulator. [ABSTRACT FROM AUTHOR]

The core idea of traditional adaptive control is to reconstruct parameter estimation errors with known signals and damping injection based on tracking error, while the formulation of desired damping in controller designs is usually a nontrivial task. The main contribution of this paper lies in the development of the classic RISE result and a constructive damping injection procedure for the adaptive tracking control of Euler–Lagrange mechanical systems. By utilizing generalized dynamic scaling function, scalar filtering, the improved RISE method and analyzing the existence of finite escape time of the closed-loop system, a globally asymptotically stable result is obtained with facilitative damping injection, significant order reduction and improved design efficiency when compared with the existing results. Simulations on a fully actuated 2-DOF planar robot manipulator model demonstrate the effectiveness of the proposed methods. • Order reduction. The extended dynamic orders of the proposed adaptive controller is less than composite adaptive RISE controller. • Performance improvement. The proposed controller achieves the global asymptotic stability with the non-CE-alike adaptive estimation performance. • Design simplification. There are many control parameters in the controller that can be adjusted to obtain the desired performance, and the computational difficulties are avoided such as analytical solution of PDE in I&I. [ABSTRACT FROM AUTHOR]

Summary: A novel adaptive predefined‐time tracking control algorithm is proposed for the Euler–Lagrange systems (ELSs) with model uncertainties and actuator faults. Compared with traditional finite‐time and fixed‐time studies, the system output tracking error under the proposed predefined‐time controller converges to a small neighborhood of zero in finite time, whose upper bound is exactly a design parameter in the control algorithm. For the uncertain model, radial‐based function neural network (RBFNN) is utilized to approximate the continuous uncertain dynamics. To deal with the actuator faults, an adaptive control law is involved in the fault‐tolerant controller. In order to achieve the predefined‐time bounded, a novel predefined‐time sliding mode surface is designed. It is proved that the tracking error vector trajectory of closed‐loop system is semi‐globally uniformly ultimately predefined‐time bounded, and the upper bounds of both the system settling time and the corresponding output tracking error can be adjusted with a simple parameter. Simulation examples finally demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

It is widely recognised that the existing parameter estimators and adaptive controllers for robot manipulators are extremely complicated, stymieing their practical use – in particular, for robots with many degrees of freedom. This is mainly due to the fact that the existing parameterisation includes the complicated signal and parameter relations introduced by the Coriolis and centrifugal forces matrix. In an insightful remark of their seminal paper, Slotine and Li suggested to use the parameterisation of the power balance equation, which avoids these terms – yielding significantly simpler designs. To the best of our knowledge, such an approach was never actually pursued in on-line implementations, because the excitation requirements for the consistent estimation of the parameters are 'very high'. In this paper, we use a recent technique of generation of 'exciting' regressors developed by the authors to overcome this fundamental problem. The result is applied to general Euler–Lagrange systems and the fundamental advantages of the new parameterisation are illustrated with comprehensive simulations of a 2 degrees-of-freedom robot manipulator. [ABSTRACT FROM AUTHOR]

Most autonomous systems can be described by Euler–Lagrange (EL) model. This article investigates the problem of prescribed time tracking control for EL systems in the presence of modeling uncertainties, prescribed performance requirements and time‐varying state constraints. Two proportional–integral (PI)‐like control schemes with time‐varying gains are developed with several favorable features: (1) achieving prescribed tracking precision within finite time in the presence of modeling uncertainties; (2) state constraints being obeyed all the time; (3) both the final tracking accuracy and the setting time being preassigned irrespective of initial condition or any other constraining parameter; and (4) bearing simple PI structure with analytical formula for robust‐adaptive tuning gains, and demanding inexpensive online computation. The benefits and effectiveness of the proposed control are also validated via numerical simulation. [ABSTRACT FROM AUTHOR]

Summary: In this article, we investigate the performance‐guaranteed tracking control for Euler–Lagrange (EL) systems subject to input saturation and output constraints. The prescribed performance and output constraints are first considered for EL systems with input saturation. Time‐varying barrier Lyapunov function (BLF) is employed to ensure constraint satisfaction. An adaptive control method for EL systems with saturation is put forward by adding a speed transformation into the BLF and designing auxiliary variables to the system. Subsequently, neural network is introduced to compensate for uncertainties of systems. In combination with backstepping technique, it is demonstrated that the controller not only guarantees that the tracking error converges to a preset compact set near zero at a specified decay rate, but also ensures that the output always stays within a given boundary. Simulation results further demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This brief investigates the predefined-time bipartite consensus of multiple Euler-Lagrange systems with a dynamic leader. A new distributed predefined-time observer is added to estimate the desired velocity of each follower. Then, a new sliding surface and a distributed protocol are constructed to guarantee the networked systems achieve the bipartite consensus within a predefined time. It should be pointed out that, all the observing time, sliding time and reaching time can be preset in advance according to the task requirements. One numerical example with two-link robot arms is proposed to verify the effectiveness of the new designs. [ABSTRACT FROM AUTHOR]

In this paper, the constrained Nash equilibrium seeking problem of aggregative games is investigated for uncertain nonlinear Euler-Lagrange (EL) systems under unbalanced digraphs, where the cost function for each agent depends on its own decision variable and the aggregate of all other decisions. By embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the digraph Laplacian matrix, a dynamic adaptive average consensus protocol is employed to estimate the aggregate function in the unbalanced case. To solve the constrained Nash equilibrium seeking problem, an integrated distributed protocol based on output-constrained nonlinear control and projected dynamics is proposed for uncertain EL players to reach the Nash equilibrium. The convergence analysis is established by using variational inequality technique and Lyapunov stability analysis. Finally, a numerical example in electricity market is provided to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the constrained Nash equilibrium seeking problem of aggregative games is investigated for uncertain nonlinear Euler-Lagrange (EL) systems under unbalanced digraphs, where the cost function for each agent depends on its own decision variable and the aggregate of all other decisions. By embedding a distributed estimator of the left eigenvector associated with zero eigenvalue of the digraph Laplacian matrix, a dynamic adaptive average consensus protocol is employed to estimate the aggregate function in the unbalanced case. To solve the constrained Nash equilibrium seeking problem, an integrated distributed protocol based on output-constrained nonlinear control and projected dynamics is proposed for uncertain EL players to reach the Nash equilibrium. The convergence analysis is established by using variational inequality technique and Lyapunov stability analysis. Finally, a numerical example in electricity market is provided to validate the effectiveness of the proposed method.

The goal of this paper is to find a stabilizing and optimal control policy for a class of systems dictated by Euler–Lagrange dynamics, that also satisfies predetermined response criteria. The proposed methodology builds upon two stages. Initially, a neural network is trained online via an iterative process to capture the system dynamics, which are assumed to be unknown. Subsequently, a successive approximation algorithm is applied, employing the acquired dynamics from the previous step, to find a near-optimal control law that takes into consideration prescribed performance specifications, such as convergence speed and steady-state error. In addition, we concurrently guarantee that the system evolves exclusively within the compact set for which sufficient approximation capabilities have been acquired. Finally, we validate our claims through various simulated studies that confirm the success of both the identification process and the minimization of the cost function.

This paper investigates the containment control problem for multiple Euler–Lagrange systems with unknown time-varying disturbances over directed graphs, in which the dynamics of leaders and followers are heterogeneous. First of all, the expected output signals of leaders can only be acquired by some subsystems owing to the limited communication conditions, and the output adjustment errors are obtained indirectly by other subsystems through the network connection. In consequence, a compensator based on relative output information is designed to estimate a trajectory inside the convex hull spanned by states of the leaders. Second, a fully distributed event-triggered adaptive control scheme is proposed, and a disturbance estimator is designed to achieve interference suppression. In addition, the design of the overall control protocol does not use the relative speed of the followers. Finally, a dual-axis manipulator is taken as an example to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper studies global robust tracking of uncertain Euler-Lagrange systems with input disturbances. The authors develop a robust regulation-based approach for the problem. Specifically, by introducing a novel nonlinear internal model, the authors solve global asymptotic trajectory tracking with disturbance rejection of multiple step/sinusoidal signals with unknown amplitudes, frequencies, and phases. Moreover, the authors show that a robustness property to actuator noises can be guaranteed in a sense of strong integral input-to-state stability (iISS). That is, the closed-loop system is not only iISS but also input-to-state stable (ISS) to small magnitude actuator noises. Furthermore, the authors explore a by-product overparametrized linear regression estimation, coming up with robust estimation of the unknown parameters. Finally, the authors present several numerical examples to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

The consensus problem based on full state feedback has been extensively studied, but rarely for leaderless distributed finite-time consensus of networked Euler-Lagrange systems based on output-feedback. In this work, the finite-time consensus problem of networked Euler-Lagrange systems subject to unknown velocity is studied. A finite-time consensus protocol is first proposed based on the relative positions and velocities. Then, the more challenging situation of networked Euler-Lagrange systems subject to unmeasurable velocity is considered. A model-independent observer based on the super-twisting algorithm (STA) is developed for velocity error estimation, based upon which a finite-time output feedback control protocol is developed for consensus of the networked Euler-Lagrange systems. Stability analysis shows that the networked Euler-Lagrange systems can achieve consensus in finite time. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed control algorithms. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aggregative games are addressed in this article, in which there are coupling constraints among decisions and the players have Euler–Lagrange (EL) dynamics. On the strength of gradient descent, state feedback, and dynamic average consensus, two distributed algorithms are developed to seek the variational generalized Nash equilibrium (GNE) of the game. This article analyzes the convergence of two algorithms by utilizing singular perturbation analysis and variational analysis. The two algorithms exponentially and asymptotically converge to the variational GNE of the game, respectively. Moreover, the results are applied to the electricity market games of smart grids. By the algorithms, turbine-generator systems can seek the variational GNE of electricity markets autonomously. Finally, simulation examples verify the methods. [ABSTRACT FROM AUTHOR]

Based on the framework of distributed optimization algorithms, this brief studies distributed optimal formation behaviors of multi-agent systems modeled as a group of uncertain Euler-Lagrange systems with collision avoidance. Assume that each agent can only obtain measured position-based gradient value of a local objective function. By integrating a modified distributed optimization algorithm and an adaptive control law, the proposed distributed optimal formation controllers can lead the positions of agents asymptotically converging to the optimal solution to the total objective function with collision avoidance. The proposed design is verified by a numerical example of mobile relays for communication. [ABSTRACT FROM AUTHOR]

We investigate a distributed time-varying formation control problem for an uncertain Euler–Lagrange system. A time-varying optimization-based approach is proposed. Based on this approach, the robots can achieve the expected formation configuration and meanwhile optimize a global objective function using only neighboring and local information. We consider the time-varying optimization where the objective functions can change in real time. In this case, the consensus-based formation tracking control issues and formation containment tracking control issues in the literature can be solved by the proposed approach. By a penalty-based method, the robots’ states asymptotically converge to the estimated optimal solution to an equivalent time-varying optimization problem, whose optimal solution can achieve simultaneous formation and optimization. Furthermore, we consider two more general scenarios: 1) the local objective functions can have non-neighbor’s information and 2) the optimization problems can have inequality constraints. [ABSTRACT FROM AUTHOR]

Motivated by the promising applications of multiple Euler–Lagrange (EL) systems, we study, in this article, the formation-containment (FC) control problem for multiple EL systems of leaders with bounded unknown control inputs and with communication among each other over directed topologies, which can cooperatively generate safe trajectories to avoid obstacles. Given the FC shapes, an algorithm is first proposed to obtain the stress matrix while satisfying certain conditions, based on which a novel adaptive distributed observer to the convex hull is proposed for every follower. An adaptive updating gain is applied to make the observer fully distributed without using the global information of the graph, and a continuous function is designed to restrain the influence of the inputs of the leaders. Then, a local control law using the adaptive distributed observer is presented to accomplish the FC control of EL systems. Based on the Lyapunov stability theory, it is proved that the FC error can be designed as small as possible by adjusting some parameters in the observer. [ABSTRACT FROM AUTHOR]

This article studies the robust tracking control problem for a class of uncertain Euler–Lagrange systems. An adaptive sliding mode control strategy is proposed to address the robust stability of the closed‐loop systems with external disturbances and parameter uncertainties. An adaptive parameter estimator is constructed in the sensor node to deal with the unknown bound of uncertainties, and an event‐triggering detector is located between the sensor node and the controller node. The introduction of event‐triggering condition is introduced, reducing the utilization on communication resources and the number of control execution. In this event‐triggered strategy, the closed‐loop systems reach the practical sliding mode band and the band could be adjusted. Moreover, the event‐triggering condition can make sure that Zeno behavior does not occur. Finally, simulation results on 2‐link robotic manipulator are provided to illustrate the effectiveness and feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear estimator-based funnel perturbation rejection control method is investigated to manage the trajectory tracking problem of a class of perturbed Euler-Lagrange (EL) systems. To reinforce the perturbation rejection ability, perturbation estimators with nonlinear dynamics are established by employing a filtering operation, which can result in asymptotic convergence of estimation errors. Besides, by devising funnel variables with an exponential decaying function, a funnel control strategy is constructed to ensure tracking errors restricting into a prescribed region under the influence of persistent perturbations. Moreover, the tracking errors of the Euler-Lagrange system are concluded to be asymptotic stability with prescribed performance via Lyapunov stability theory. Finally, simulations validate the effectiveness of the developed control technology. • The asymptotic trajectory tracking and perturbation rejection problems of Euler Lagrange systems are addressed. • A novel nonlinear dynamics estimator is investigated to estimate the perturbations with higher estimation accuracy. • The system performances of convergence time, overshoot, and steady precision are governed by funnel control designs. • The superiority of the proposed control strategies is substantiated by simulation results of a quadrotor aircraft system. [ABSTRACT FROM AUTHOR]

Reinforcement learning (RL) has enjoyed considerable success in application to nonlinear systems. However, very few RL-based works that explicitly address the control problem of MIMO nonlinear systems with subject to actuator failures. In this work, we develop a fault-tolerant adaptive tracking control method fused with an echo state network (ESN) driven by reinforcement learning for Euler-Lagrange systems subject to actuation faults. The proposed control includes an associative search network (ASN), a control gain network (CGN), and an adaptive critic network (ACN), with ASN to estimate the unknown items of the control system, CGN to deal with the time-varying and unknown control gains matrix, and ACN to generate the reinforcement signal, all together ensuring stable tracking and accommodate modeling uncertainties and actuation failures. Different from traditional reinforcement learning controllers that utilizes radial basis function neural networks (RBFNN) or fuzzy systems, the proposed one adopts an echo state network, a paradigm of recurrent neural networks, to implement the ASN, ACN and CGN, resulting in enhanced learning capabilities and stronger robustness against external uncertainties and disturbances, thus better control performance. [ABSTRACT FROM AUTHOR]

This paper provides two bounded finite-time control strategies for the stabilization problem of Euler–Lagrange (EL) systems exposed to actuator failures. By the combination of sliding mode technology and adaptive method, two control architectures have been constructed such that the system states will be forced towards the origin within finite time. The first controller is applicable in the case that exact information of the external disturbance and actuator faults are available. However, it still remains challenging for designers to obtain this sort of information in engineering practice. On account for this, adaptive laws are applied in the second controller to obtain estimations about the unknown parameters, thus ensuring desirable fault-tolerance ability and robustness for the EL systems. By resorting to the properties of EL systems and hyperbolic tangent functions, outputs of these two controllers will be proven to be bounded. Simulation examples are presented to manifest the validity of the developed algorithms. [ABSTRACT FROM AUTHOR]

The problem of tracking uncertain target is interesting and challenging. This paper studies the target tracking control problem of Euler–Lagrange system with unknown target trajectory. Fourier series and neural network are utilized to reconstruct the target trajectory, which is mathematically linked with the actual camouflaged target trajectory and facilitates the design and analysis. An error transformation function is introduced and embedded with the Lyapunov function, with which an adaptive tracking control scheme is developed. It is shown that such strategy is able to ensure the tracking error converging to a prescribed compact set containing the origin at a self-defined convergence rate. The simulation results verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, we present an inverse optimal tracking controller for a class of Euler–-Lagrange systems having uncertainties in their dynamical terms under the restriction that only the output state (i.e. position for robotic systems) is available for measurement. Specifically, a nonlinear filter is used to generate a velocity substitute, then a controller formulation ensuring a globally asymptotically stable closed-loop system while minimizing a performance index despite the presence of parametric uncertainty, is proposed. The stability proof is established using a Lyapunov analysis of the system with proposed optimal output feedback controller. Inverse optimality is derived via designing a meaningful cost function utilizing the control Lyapunov function. Numerical simulations are presented to illustrate the viability and performance of the derived controller. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem of a multi-Euler-Lagrange system is studied under deception attacks, where attackers can inject the false data into the data being exchanged over the communication network between two Euler-Lagrange systems. A distributed adaptive filter is proposed to compensate the unknown injection false data, where the magnitude of the false data is estimated. Meanwhile, the performance of the multiple Euler-Lagrange system consensus with the proposed filter can be guaranteed to be similar to that with the traditional controller when the communication network is not injected into false data by a malicious attacker. Furthermore, the consensus criteria of a multiple Euler-Lagrange system and the parameter design scheme of the proposed adaptive filter are achieved by using Lyapunov stability theory. Finally, a numerical example is carried out to demonstrate the effectiveness of the proposed consensus controller for a multi-Euler-Lagrange system attacked by using the false data injection.

This article addresses the formation control problem of flapping-wing vehicles (FWVs) under the model uncertainty and the measurement inaccuracy. A two-layer formation strategy is adopted, which consists of a formation control layer for the leaders, and a containment control layer for the followers. In both layers, attitudes and positions are required by the formation geometry. A formation state estimation algorithm is designed to achieve the desired formation states from local neighborhoods. In FWVs, attitude angles are usually achieved from angular velocities, whose measurement error accumulates during integration and leads to divergence of the system. In order to solve this problem, we explore the coupling property between the translational motion and the rotational motion of FWVs, and design a coupling-based estimation method for attitude angles. To compensate for the model uncertainty, the measurement error, and the estimation error, adaptive neural networks are developed together with the control algorithm. The stability of both the control algorithm and the estimation algorithm is guaranteed based on the Lyapunov stability theory. Simulations are conducted to validate our method, and the results illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

A distributed event-triggered protocol is proposed to deal with the time-varying formation control problem of Euler–Lagrange systems with uncertain model parameters in this research. By utilizing the small-gain theorem and matrix transformation, we show the input–output stability of the closed-loop cascade system with Euler–Lagrange dynamics. An event-triggered condition (ETC) is designed by only using the local information of each agent, which avoids the continuous communication in the event detection and excludes the Zeno behavior. Finally, the proposed methods are applied to the practical flight platform for quadrotors. The experiment using three quadrotors in the outdoor environment is demonstrated to test the effectiveness of the formation protocol. [ABSTRACT FROM AUTHOR]

This article investigates an aggregative game based on Euler-Lagrange systems subject to time-varying communication delays. First, a distributed algorithm is put forward to try to find the Nash equilibrium by the deliberated group of Euler-Lagrange systems with “small” delay and “large” delay. Second, we illustrate the convergence of two circumstances, separately. The first circumstance derives the upper bound of delays for guaranteeing globally exponential convergence, and the other obtains globally exponential convergence, even in some restrictions on “large” delays. Finally, a numerical example is used to show the effectiveness and superiority of proposed method.

In this paper, a robust adaptive finite-time (FT) tracking control scheme is proposed for Euler-Lagrange systems (ELSs) subject to nonparametric uncertainties, unknown disturbances and input saturation. In the design procedure, a Gaussian error function is utilized to approximate the input saturation nonlinearity. Following that, by employing the natural property that the upper bound of model parameters uncertainties is linear-in-parameters, the lumped uncertain term caused by uncertain model parameters and external disturbances is formulated by a linear-parametric form with a single parameter. And then, a novel robust adaptive tracking control law is designed to resolve the tracking control problem of uncertain ELSs. The proposed control scheme is featured by FT convergence rate, and robustness against uncertainties and unknown disturbances. Furthermore, the robust adaptive FT tracking control scheme is insensitive to the character of the uncertainties, and is with low computational burden and easy to implement in engineering applications. And its rigorous stability is analyzed with the aid of the Lyapunov stability theory, and its effectiveness is verified by simulation results and comparison.

This paper gives a class of novel predefined-time sliding mode surfaces based on the time-regulator function, forcing the states on them to approach the origin in a predefined time, which can be employed to replace the linear sliding mode surface that is used in the existing literatures focused on the predefined-time set stabilization problems such that the zero-error predefined-time stability can be achieved. In this way, the settling time is independent of the initial conditions and can be explicitly predefined as a specific control parameter. Later, such sliding mode surfaces are utilized to construct the nonsingular sliding mode control (SMC) for both uncertain second-order systems and disturbed Euler–Lagrange systems. The sufficient conditions for the proposed control schemes to guarantee the predefined-time stability, satisfactory capability of disturbance rejection, and nonsingularity of the control input are derived through systematic stability analysis. Finally, several numerical simulations are performed on generalized uncertain second-order systems and 2-DOF (degree of freedom) robot manipulator to show the effectiveness and the performance of the presented control schemes. [ABSTRACT FROM AUTHOR]

This brief presents an even-triggered control framework for networked Euler-Lagrange systems to achieve bipartite consensus even in the presence of external disturbance. In particular, an adaptive protocol with simple distributed updating laws is proposed by combining the disturbance compensator technique. The new event-triggered control algorithm is constructed without utilizing velocity information, which mitigates the cost on distributed bipartite consensus protocol design. Additionally, there is no Zeno behaviors by giving the positive lower bounds of execution intervals. Numerical examples are applied in the end to verify the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes a strategy to overcome the threats posed to connectivity-preserving synchronization of Euler–Lagrange networks by time-varying delays and bounded actuation. It first introduces a suitable distributed negative gradient plus damping injection controller, based on which it establishes that the local connectivity of time-delay Euler–Lagrange networks can be preserved by appropriately regulating the interagent connections and increasing the damping injection locally. Yet, actuator saturation may impede the proper modulation of the interagent connections and the injection of sufficient damping and, thus, may threaten the maintenance of connectivity. This paper then develops an indirect coupling control framework which integrates the bounded actuation constraints into the control design. The framework endows every agent with a virtual proxy and couples initially adjacent agents through their virtual proxies. The interproxy couplings then tackle the time-varying delays while the agent-proxy couplings account for the saturation of actuators. Lyapunov–Krasovskii analysis proves that the indirect coupling strategy can drive time-delay Euler–Lagrange networks with bounded actuation to connectivity-preserving synchronization by limiting the energy of the agent-proxy and interproxy couplings according to the actuation constraints. Experiments with Geomagic Touch haptic robots validate the proposed designs compared to a conventional proportional plus damping controller. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered reinforcement learning-based met-hod is developed for model-based optimal synchronization control of multiple Euler-Lagrange systems (MELSs) under a directed graph. The strategy of event-triggered optimal control is deduced through the establishment of Hamilton-Jacobi-Bellman (HJB) equation and the triggering condition is then proposed. Event-triggered policy iteration (PI) algorithm is then borrowed from reinforcement learning algorithms to find the optimal solution. One neural network is used to represent the value function to find the analytical solution of the event-triggered HJB equation, weights of which are updated aperiodically. It is proved that both the synchronization error and the weight estimation error are uniformly ultimately bounded (UUB). The Zeno behavior is also excluded in this research. Finally, an example of multiple 2-DOF prototype manipulators is shown to validate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite-time distributed optimization problem for multiple Euler–Lagrange systems. A new distributed optimization control scheme is presented to achieve the state agreement in finite time while minimizing the sum of each agent’s local cost function. The proposed algorithm has the advantage of being able to achieve distributed finite-time optimization consensus under general unbalanced connected directed communication graphs. By virtue of finite-time Lyapunov theory and convex optimization, the finite-time convergence for the algorithm is analyzed. A numerical example is also presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, under-directed topology, distributed coordinated tracking control schemes are proposed for multiple Euler-Lagrange systems with time-varying communication delays, nonlinear uncertainties, and external disturbances. Concerning with different leader velocities, both constant leader velocity case and time-varying leader velocity case are addressed by designing two different distributed observers. Combining with the proposed distributed leader velocity observers, two coordinated tracking control schemes are developed by the effort of neural network approximation and sliding mode technique, which can compensate the nonlinearities and uncertainties. For the first case, tracking errors are rigorously proved to be globally asymptotically converged by using Lyapunov-Krasovskii method. To further eliminate chattering caused by the discontinuous sign function, the saturation function is used for the second case, and the proposed control algorithm ensures the same convergence of tracking errors via Lyapunov analysis. Finally, the effectiveness of the proposed distributed tracking control schemes is verified by the numerical examples.